The Estimation Of Semiparametric Poisson Mixture Regression Model

Count data with repeated measurements is widespread in the fields of biomedicine, industry, agriculture and so on. Poisson random effect model has been paid much attention by many researchers to characterize this kind of data. However, in practical problems, the count data may come from different totals and meanwhile has some unknown connection with time, so the classical Poisson random effect model may be no longer suitable. For these reasons, semiparametric Poisson mixture model is used in this paper.In this paper, firstly, we consider a semiparametric two-component Poisson mix-ture model that contains a non-parametric function in each component. The unknown function is approximated based on P-spline, and the parameter estimation of the mod-el is studied by the penalized log-likelihood function and EM algorithm. Secondly, we add bivariate random effects to the above model to characterize count data with repeat-ed measurements reasonably, and obtain the semiparametric two-component Poisson mixture model with random effects. This model can not only describe the correlation within individuals, but also account for the correlation between different components.Similarly, we deduce the penalized log-likelihood function based on P-spline, and discuss the parameter estimation of the model in the framework of MCEM algorith-m. Under certain conditions, we establish the consistency and asymptotic normality of the resulting estimators. Finally, Stochastic simulations are provided under finite sample to evaluate the effectiveness of the parameter estimation methods of two mod-el. At the same time, we use a semiparametric one-component Poisson model with random effects and a semiparametric two-component Poisson mixture model with ran-dom effects to fit a set of real data, and find that the model presented in this paper is superior to the single component semiparametric model by model selection based on AIC criterion.